# 100% chance at $1.08M or 97% at $36M? **URL:** \ **Category:** In My Humble Opinion\ **Created:** [November 22, 2017, 2:03pm UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402 "2017-11-22T14:03:31Z")\ **Posts on this page:** 20\ **Page:** 3
**Author:** ![Little\_Nemo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/little_nemo/32/3120_2.png) [@Little\_Nemo](https://boards.straightdope.com/u/Little_Nemo)\ **Post date:** [November 22, 2017, 4:48pm UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/41 "2017-11-22T16:48:35Z")
I’m going for the thirty-six million. 97% odds are good enough for me in a situation where it’s all gain. But I might avoid those odds if I had to take a risk at losing money. Say I had to buy the thirty-six chips at a thousand dollars apiece in order to spin for the thirty-six million. In that case, I’d probably take the sure thing rather than take the small chance of losing a substantial amount of my own money. Does that make sense? Rationally, no. ---
**Author:** ![watchwolf49](https://avatars.discourse-cdn.com/v4/letter/w/e9c0ed/32.png) [@watchwolf49](https://boards.straightdope.com/u/watchwolf49)\ **Post date:** [November 22, 2017, 4:49pm UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/42 "2017-11-22T16:49:48Z")
These results so far are shocking to me … _never ever_ walk away from a sure bet … also, not sure where you play roulette, but typically the house pays 35 to 1 for single number bets … so $35m instead of $37m … and North America usually runs two green slots, 0 and 00, so more like a 5.6% chance of losing all … The sure thing is $28,000 per year … why would you take on unnecessary default risk? … ---
**Author:** ![mikecurtis](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mikecurtis/32/3284_2.png) [@mikecurtis](https://boards.straightdope.com/u/mikecurtis)\ **Post date:** [November 22, 2017, 4:52pm UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/43 "2017-11-22T16:52:23Z")
> [@Velocity](#): > > …but it seems like Dopers here who are already in good financial shape are instead opting for the safe choice. that’s how they got to be in good financial shape! mc ---
**Author:** ![Corry\_El](https://avatars.discourse-cdn.com/v4/letter/c/ecae2f/32.png) [@Corry\_El](https://boards.straightdope.com/u/Corry_El)\ **Post date:** [November 22, 2017, 4:54pm UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/44 "2017-11-22T16:54:07Z")
Also hard for me to fathom how someone could think the chance of dying in an airliner crash is anything like 3% per flight\*, the real world issue it points up is that the risk isn’t actually known when you get on the plane. Malaysian airliners getting shot down over Ukraine doesn’t affect your odds on a US scheduled domestic flight. The stats for US airlines are zero fatal accidents since 2009. That doesn’t mean the chance of the plane arriving safely is 100% (and you could die of a medical condition during the flight though the plane arrives safely), but you don’t really know what the odds are. Practically you know they’re _way_ less than 3% per flight. But, there are other risks, including ones in investing which are closer to the question, that might be similar to 3% but you don’t actually know what they are. People quote statistics for the ‘probability’ of total market meltdowns etc, but that’s just what _has_ happened. The future odds aren’t any more certainly known than the outcomes themselves. That’s different than accepting known odds in the OP case. \*which seemed to be implied; the total life long chance could be that order of magnitude I guess if you did a lot of flying on scheduled airliners in the most unsafe countries for years, small planes and helo’s to difficult and remote locations, etc. again cumulative probability over your life time. ---
**Author:** ![Machine\_Elf](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@Machine\_Elf](https://boards.straightdope.com/u/Machine_Elf)\ **Post date:** [November 22, 2017, 4:55pm UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/45 "2017-11-22T16:55:27Z")
> [@Velocity](#): > > If the OP had said, “Would you take a 97% chance of winning $1.025 million, rather than a guaranteed $1 million,” I’d probably go for the guaranteed money. :dubious: In that scenario, the expected value of the first choice is only $994K; you’d have to have some kind of risk fetish to take that option instead of the for-sure $1M. Most people pay to _reduce_ their risk, not increase it. > [@Velocity](#): > > So to go by your analogy - if someone said “97% chance of arriving safely but you get ten thousand dollars,” or “100% chance of arriving safely but you get no bonus money,” I’d take the 97%. :dubious: Really? You’d accept a one-in-thirty chance of death for a payout of $10K? Either you are frightfully poor and desperate for cash, or you hold your life to be of uncommonly low worth. > [@Velocity](#): > > By the way, if someone said, “Your chances of dying tomorrow are 97%” vs. “Your chances of dying tomorrow are 100%,” you’d be in pretty bad shape either way. True enough, but if someone gave me a choice between the two, I wouldn’t shrug and say “97% is virtually the same as 100%, so it doesn’t matter which one I choose.” ---
**Author:** ![Sir\_T-Cups](https://avatars.discourse-cdn.com/v4/letter/s/ed655f/32.png) [@Sir\_T-Cups](https://boards.straightdope.com/u/Sir_T-Cups)\ **Post date:** [November 22, 2017, 4:55pm UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/46 "2017-11-22T16:55:36Z")
As has been stated: 97% is virtually 100%, and makes this decision basically a no-brainer. ETA: I’m in the minority here that 1M, even the 600 after taxes, would absolutely be life-changing to me. I couldn’t quit my job or anything, but it would eliminate all my debt, allow me to instantly advance my life and overall make living so, so much easier. That being said, I’m STILL playing the odds ---
**Author:** ![Corry\_El](https://avatars.discourse-cdn.com/v4/letter/c/ecae2f/32.png) [@Corry\_El](https://boards.straightdope.com/u/Corry_El)\ **Post date:** [November 22, 2017, 5:06pm UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/47 "2017-11-22T17:06:27Z")
> [@Velocity](#): > > This isn’t a valid way to look at it without the other option provided by the OP, since it’s framed as one of two choices. Yes I agree, the 97% likely to arrive safely airliner case (assuming it could be determined those were the much lower than recent historical odds) doesn’t offer an alternative except the implied one of just staying home, you didn’t need to go anyway. The OP case offers one case with a rough expected value (ignoring taxes) of $1mil, and another with an expected value of $34.9mil (.97\*36). You either give up 33.9mil in expected value to reduce risk, or not. It is though IMO useful to try to compare it to risks you take otherwise, including ones you can’t avoid, like dying tragically young from a medical condition or accident. That’s more than 3% depending how you define ‘dying young’. I personally can’t fathom leaving that kind of expected value on the table when there’s at least an equal chance of various much worse things happening to me than walking away empty handed from that bet. But as mentioned before and all seem to agree, depends how big that smaller windfall is, and one’s own existing resources. I assume a lot fewer people would go for the sure thing at one grand v 97% chance at 36 grand, and a lot more would go for it at 100mil v $3.6bil. I can’t see any good basis for a blanket rule ‘always go with the sure thing’ though. ---
**Author:** ![Mr\_Shine](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mr_shine/32/464_2.png) [@Mr\_Shine](https://boards.straightdope.com/u/Mr_Shine)\ **Post date:** [November 22, 2017, 5:13pm UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/48 "2017-11-22T17:13:49Z")
I don’t think my poll options were confusing at all, but I note **BigT, RivkahChaya** and **Crotalus** , (possibly others: I haven’t exhaustively checked, those names just stood out) have all voted in the poll in the opposite way to the way they indicated in the thread. ---
**Author:** ![kayaker](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kayaker/32/441_2.png) [@kayaker](https://boards.straightdope.com/u/kayaker)\ **Post date:** [November 22, 2017, 5:19pm UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/49 "2017-11-22T17:19:49Z")
> [@Mr\_Shine](#): > > I don’t think my poll options were confusing at all, but I note **BigT, RivkahChaya** and **Crotalus** , (possibly others: I haven’t exhaustively checked, those names just stood out) have all voted in the poll in the opposite way to the way they indicated in the thread. They shouldn’t get any money then. Can I have theirs? Please? ---
**Author:** ![blondebear](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/blondebear/32/1022_2.png) [@blondebear](https://boards.straightdope.com/u/blondebear)\ **Post date:** [November 22, 2017, 5:30pm UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/50 "2017-11-22T17:30:32Z")
I’ll take the million, or 600K, or whatever it ends up being after taxes. Bird in the hand and all that. ---
**Author:** ![gnoitall](https://avatars.discourse-cdn.com/v4/letter/g/bb73d2/32.png) [@gnoitall](https://boards.straightdope.com/u/gnoitall)\ **Post date:** [November 22, 2017, 5:40pm UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/51 "2017-11-22T17:40:01Z")
> [@bucketybuck](#): > > Thats just horribly insane logic. I get not wanting to manage a portfolio or something like that, but whats to manage about taking the money and letting it sit in a bank account? > > A full time job safeguarding and keeping watch on money just sitting there being numbers on a page? Really? And why would your opinion matter to me? ---
**Author:** ![DrDeth](https://avatars.discourse-cdn.com/v4/letter/d/b487fb/32.png) [@DrDeth](https://boards.straightdope.com/u/DrDeth)\ **Post date:** [November 22, 2017, 5:42pm UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/52 "2017-11-22T17:42:26Z")
> [@blondebear](#): > > I’ll take the million, or 600K, or whatever it ends up being after taxes. Bird in the hand and all that. Yep. It would pay off the mortage, and make my eventual retirement worry free. ---
**Author:** ![Machine\_Elf](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@Machine\_Elf](https://boards.straightdope.com/u/Machine_Elf)\ **Post date:** [November 22, 2017, 6:19pm UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/53 "2017-11-22T18:19:58Z")
> [@gnoitall](#): > > And why would your opinion matter to me? I think his point is that your assessment of how much work is involved in possessing $37M might be flawed. Upthread: > [@Corry El](#): > > PS if anyone would _really_ turn down 10’s of mils because ‘hard to manage’, I hope they educate themselves before it ever happens to them. One ‘all-in-one’ Vanguard fund, few 0.1%'s at most expenses, they manage the rebalancing between asset classes, then open four savings accounts with a few clicks each to have a ready $1mil at all times ($250k FDIC gtee limit per account), done. That’s going to ruin somebody’s life with stress, seriously? This doesn’t seem like any more work than what I’m doing right now to manage my (much smaller) nest egg. ---
**Author:** ![Voyager](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/voyager/32/133_2.png) [@Voyager](https://boards.straightdope.com/u/Voyager)\ **Post date:** [November 22, 2017, 6:27pm UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/54 "2017-11-22T18:27:24Z")
Definitely the $37 million. A million more right now would not change my life at all. $37 million would let me fly first class and other such wastes of money. I’ve already got a financial planner, so I’d just meet with him about where to put the cash - income generating investments, mostly, which is where a lot of my money is now. OP, it would be interesting if you redid the experiment with a 3% chance of getting nothing as opposed to 97% chance of a gain. ---
**Author:** ![Voyager](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/voyager/32/133_2.png) [@Voyager](https://boards.straightdope.com/u/Voyager)\ **Post date:** [November 22, 2017, 6:30pm UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/55 "2017-11-22T18:30:10Z")
> [@bucketybuck](#): > > What is its current odds of arriving safely? Because damn sure it’s already less than 100%, and I wouldn’t be surprised to find that current odds were already less than 97%. I suspect many people working in Judgement Decision Making research would love to talk to you to find out the source of your fallacy. Is it not seeing how far 97% is from 99.999%? Is it availability - you’ve read too much about airplane crashes? ---
**Author:** ![puzzlegal](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/puzzlegal/32/3827_2.png) [@puzzlegal](https://boards.straightdope.com/u/puzzlegal)\ **Post date:** [November 22, 2017, 6:30pm UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/56 "2017-11-22T18:30:40Z")
I’d put a big “it’s a scam” discount on this game. But for the sake of entertainment, I’ll assume that I believe those are actually the two choices. > [@Steve\_MB](#): > > I’d try for the $36 million. A little over $1 million would allow a few luxuries but mostly fatten my already adequate retirement savings; $36 million, handled with reasonable prudence, would be take-this-job-and-shove-it followed by a very comfortable lifestyle money. Pretty much this. I already have other options if I decide to quit my job, so I wouldn’t “take this job and shove it”. But I’m on track to a comfortable retirement without the added million. Whereas an additional $36m would open up some options I don’t have today. Maybe a nice brownstone in Manhattan, for example. It would also mean I could stop worrying about my unemployed (and possibly unemployable) daughter’s future. ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [November 22, 2017, 6:42pm UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/57 "2017-11-22T18:42:06Z")
> [@Mr\_Shine](#): > > I don’t think my poll options were confusing at all Actually, they are a little confusing, or at least I see the potential for immediate confusion. I had to double check to make sure I read the options and the hypothetical correctly. The confusing part is both options and outcomes contain the numbers 37 and 1, but don’t correspond to each other. If you’d go for the $37 million, you have to choose the second option, which contains the phrase “$1 million,” while the “take the $1 million” option is the one with the number 37 in it. ---
**Author:** ![bucketybuck](https://avatars.discourse-cdn.com/v4/letter/b/898d66/32.png) [@bucketybuck](https://boards.straightdope.com/u/bucketybuck)\ **Post date:** [November 22, 2017, 6:47pm UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/58 "2017-11-22T18:47:53Z")
> [@Machine\_Elf](#): > > If the odds of a plane flight arriving safely were less than 97%, there would be [thousands of plane crashes every day.](https://www.google.com/search?q=number%20of%20flights%20per%20day&cad=h) Maybe I’m not tapped into the right news sources, but I think the number of crashes per day is much, much less than “thousands”. So I don’t carry knowledge of the number of plane crashes around in my head, fair enough, but I would have thought it obvious that whatever the percentage was didn’t matter to the important point, which was the fact that there is already a risk to taking a flight, same as there is to any journey. > [@gnoitall](#): > > And why would your opinion matter to me? You seem to have missed the point. Still, if you would pass on an easy 36 million because you would find it hard to put into a savings account then that is of course your privilege. ---
**Author:** ![AlsoNamedBort](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/alsonamedbort/32/3213_2.png) [@AlsoNamedBort](https://boards.straightdope.com/u/AlsoNamedBort)\ **Post date:** [November 22, 2017, 6:49pm UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/59 "2017-11-22T18:49:38Z")
I’d be interested to know, for the people that took the sure thing: Let’s say we took a chip off both sides, so now it’s at 97.3% chance of winning a million and a 94.6% of winning 36 million. Does that change your mind? If not, lets say we continue removing a chip from each side. Is there a point where you would go for the 36 million instead? ---
**Author:** ![puzzlegal](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/puzzlegal/32/3827_2.png) [@puzzlegal](https://boards.straightdope.com/u/puzzlegal)\ **Post date:** [November 22, 2017, 6:51pm UTC](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402/60 "2017-11-22T18:51:05Z")
> [@Mr\_Shine](#): > > I don’t think my poll options were confusing at all, but I note **BigT, RivkahChaya** and **Crotalus** , (possibly others: I haven’t exhaustively checked, those names just stood out) have all voted in the poll in the opposite way to the way they indicated in the thread. Really? I initially read this on my phone, and didn’t see the poll. But I just looked on my laptop, and I had to stare and think hard about it (and didn’t vote, because I wanted to make sure.) > [@pulykamell](#): > > Actually, they are a little confusing, or at least I see the potential for immediate confusion. I had to double check to make sure I read the options and the hypothetical correctly. The confusing part is both options and outcomes contain the numbers 37 and 1, but don’t correspond to each other. If you’d go for the $37 million, you have to choose the second option, which contains the phrase “$1 million,” while the “take the $1 million” option is the one with the number 37 in it. This. Especially since the the first one doesn’t say what the chips are worth, and the second one looks like $1M if read quickly. [Previous page](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402.md?page=2) [Next page](https://boards.straightdope.com/t/100-chance-at-1-08m-or-97-at-36m/802402.md?page=4)